Quantum Inf Process (2015) 14:1809–1825
A new quantum scheme for normal-form games
Received: 20 December 2014 / Accepted: 18 March 2015 / Published online: 2 April 2015
© The Author(s) 2015
Abstract We give a strict mathematical description for a reﬁnement of the Marinatto–
Weber quantum game scheme. The model allows the players to choose projector
operators that determine the state on which they perform their local operators. The
game induced by the scheme generalizes ﬁnite strategic-form game. In particular, it
covers normal representations of extensive games, i.e., strategic games generated by
extensive ones. We illustrate our idea with an example of extensive game and prove
that rational choices in the classical game and its quantum counterpart may lead to
signiﬁcantly different outcomes.
Keywords Normal-form game · Centipede game · Quantum game · Nash
A 15-year-period research on quantum games results in many ideas of how a quantum
game might look like and how it might be played. Certainly, the quantum scheme
for 2 × 2 games introduced in  (the EWL scheme) has become one of the most
common models and it has already found application in more complex games (see, for
example, ). However, the more complex the classical game is, the more sophisticated
techniques are required to ﬁnd optimal players’ strategies in the EWL-type scheme.
While in the scheme for 2 × 2 games the result of the game depends on six real
The project was supported by the Grant for Young Researchers 2014–15, Pomeranian University.
Institute of Mathematics, Pomeranian University, ul. Arciszewskiego 22d, 76-200 Słupsk, Poland